Zhusubaliyev Zhanybai T, Mosekilde Erik, De Soma, Banerjee Soumitro
Kursk State Technical University, Department of Computer Science, 50 Years of October Street, 94, Kursk 305040, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026206. doi: 10.1103/PhysRevE.77.026206. Epub 2008 Feb 11.
Recent work has shown that torus formation in piecewise-smooth maps can take place through a special type of border-collision bifurcation in which a pair of complex conjugate multipliers for a stable cycle abruptly jump out of the unit circle. Transitions from an ergodic to a resonant torus take place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic bifurcations, can involve mechanisms that differ qualitatively from those described by Afraimovich and Shilnikov.
最近的研究表明，分段光滑映射中的环面形成可以通过一种特殊类型的边界碰撞分岔发生，在这种分岔中，稳定周期的一对复共轭乘数突然跳出单位圆。从遍历环面到共振环面的转变通过边界碰撞折叠分岔发生。我们研究了此类映射中环面破坏导致的混沌转变。考虑一个分段线性范式映射，我们表明，由于边界碰撞分岔与倍周期分岔和同宿分岔的相互作用，这种转变可能涉及与阿夫拉伊莫维奇和希利尼科夫所描述的机制在性质上不同的机制。
